Solve for x square root of 8x-1 = square root of 3-4x

$\sqrt{8 x - 1} = \sqrt{3 - 4 x}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{8 x - 1}}^{2} = {\sqrt{3 - 4 x}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x - 1}$ as ${(8 x - 1)}^{\frac{1}{2}}$ .

${({(8 x - 1)}^{\frac{1}{2}})}^{2} = {\sqrt{3 - 4 x}}^{2}$

Simplify the left side.

Simplify ${({(8 x - 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 x - 1)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(8 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 - 4 x}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 - 4 x}}^{2}$

Rewrite the expression.

${(8 x - 1)}^{1} = {\sqrt{3 - 4 x}}^{2}$

Simplify.

$8 x - 1 = {\sqrt{3 - 4 x}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 - 4 x}}^{2}$ as $3 - 4 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 - 4 x}$ as ${(3 - 4 x)}^{\frac{1}{2}}$ .

$8 x - 1 = {({(3 - 4 x)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 x - 1 = {(3 - 4 x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$8 x - 1 = {(3 - 4 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$8 x - 1 = {(3 - 4 x)}^{\frac{2}{2}}$

Rewrite the expression.

$8 x - 1 = {(3 - 4 x)}^{1}$

Simplify.

$8 x - 1 = 3 - 4 x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $4 x$ to both sides of the equation.

$8 x - 1 + 4 x = 3$

Add $8 x$ and $4 x$ .

$12 x - 1 = 3$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$12 x = 3 + 1$

Add $3$ and $1$ .

$12 x = 4$

Divide each term in $12 x = 4$ by $12$ and simplify.

Divide each term in $12 x = 4$ by $12$ .

$\frac{12 x}{12} = \frac{4}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{4}{12}$

Divide $x$ by $1$ .

$x = \frac{4}{12}$

Simplify the right side.

Cancel the common factor of $4$ and $12$ .

Factor $4$ out of $4$ .

$x = \frac{4 (1)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 1}{4 \cdot 3}$

Cancel the common factor.

$x = \frac{4 \cdot 1}{4 \cdot 3}$

Rewrite the expression.

$x = \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$

Solve for x square root of 8x-1 = square root of 3-4x

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